Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to 256×256. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a 12× inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by 23.1% in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.
Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.
Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20× speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.
Flow Matching (FM) is a simulation-free method for learning a continuous, invertible flow that interpolates between two distributions, and in particular generates data from noise. Inspired by the variational nature of the diffusion process as a gradient flow, we introduce a stepwise FM model, Local Flow Matching (LFM), which sequentially learns a sequence of FM submodels, each matching a diffusion process up to the time-step size in the data-to-noise direction. In each step, the two distributions to be interpolated by the sub-flow model are closer than those in the full-flow matching model, which interpolates data to noise distributions, enabling smaller models with more efficient training. This variational perspective also allows us to prove a theoretical generation guarantee for the proposed flow model in terms of the χ2-divergence between the generated and true data distributions, leveraging the contraction property of the diffusion process. In practice, the stepwise structure of LFM is naturally amenable to model distillation, and various distillation techniques can be applied to accelerate generation. We empirically demonstrate that LFM achieves competitive generative performance compared to FM on unconditional generation of tabular and image datasets, and on conditional generation of robotic manipulation policies.